As illustrated in the accompanying figure, suppose thattwo observers are stationed at

Chapter 10, Problem 46

(choose chapter or problem)

As illustrated in the accompanying figure, suppose that two observers are stationed at the points \(F_{1}(c, 0)\) and \(F_{2}(-c, 0)\) in an xy-coordinate system. Suppose also that the sound of an explosion in the -plane is heard by the \(F_{1}\) observer t seconds before it is heard by the \(F_{2}\) observer. Assuming that the speed of sound is a constant v, show that the explosion occurred somewhere on the hyperbola

\(\frac{x^{2}}{v^{2} t^{2} / 4}-\frac{y^{2}}{c^{2}-\left(v^{2} t^{2} / 4\right)}=1\)

Equation Transcription:

Text Transcription:

F_1(c, 0)

F_2(-c, 0)

F_1

F_2

x^2 /v^2 t^2 /4 -y^2 /c^2 -(v^2 t^2 /4) =1